Computing with Quantum Cats (32 page)

Entanglement apparatus in the lab of Anton Zeilinger, Vienna.

Quantum physics at work: an MRI scanner in operation.

John Bell, who stimulated research that proved the world does not conform to local reality.

David Bohm, who challenged conventional quantum wisdom.

Hans Dehmelt, who shared the 1989 Nobel Prize in physics for his work with ion traps.

Alain Aspect, who measured the Bell inequalities.

Brian Josephson celebrates the news of his share of the Nobel Prize in 1973.

David Wineland
(left)
and Serge Haroche, the joint winners of the 2012 Nobel Prize in physics.

Wineland with an ion trap device.

World chess champion Gary Kasparov
(right)
ruminates before making his first move in a chess game against the computer Deep Blue, 1997. Deep Blue won the series 3½–2½.

Ion trap laboratory at the University of Sussex. The inset shows the “chip” itself, with electrodes 2 micrometers thick and 130 micrometers wide, at the heart of the experiment.

Getting from ENIAC to the iPhone took less than a human lifetime—threescore years and ten. If quantum computer technology is tamed, the next 70 years will see even greater advances.

INTRODUCTION: COMPUTING WITH QUANTUM CATS

1
. The discussion here borrows from the one in my book
In Search of the Multiverse
, which I could not improve upon.

CHAPTER 1: TURING AND THE MACHINE

1
. She was christened Ethel Sara, but preferred Sara.

2
. Information about Alan's childhood, here and later, from Sara Turing's memoir,
Alan M. Turing
.

3
. This proved more useful than earlier prizes he had received while at school, mostly in the form of literary works. These books are now in the museum at Bletchley Park, and show little sign of ever having been read.

4
. Gian-Carlo Rota, quoted by Leavitt,
The Man Who Knew Too Much
.

5
. Quoted by Dyson,
Turing's Cathedral
.

6
. Letter quoted by Hodges,
Alan Turing
.

7
. I oversimplify greatly; for the full story, see Jack Copeland and others,
Colossus
.

8
. Through his contacts with GC&CS, Turing was already aware of, and had done a considerable amount of work on, Enigma while still in Cambridge, with occasional visits to GC&CS: see Copeland (ed.),
The Essential Turing
.

9
. Simon Singh,
The Code Book
.

10
. The process involved, apart from the encipherment, converting analogue signals into digital form and back again, as in the conversion of music into MP3 files and back again. My own Turing machine is doing this as I write.

11
. Of course, messages could also be sent in real time, letter by letter as the operators typed; they would use this method to make contact before running a prepared paper tape through the transmitter.

12
. Flowers, quoted in Copeland and others,
Colossus
.

13
. From the initials of Women's Royal Naval Service.

14
. Copeland and others,
Colossus
.

15
.
http://www.AlanTuring.net/tunny_report
.

16
. Not that Turing cared much for such honors; he kept the medal in a tin box along with an assortment of nails, screws and other odds and ends.

17
. Quoted in Lavington (ed.),
Alan Turing and His Contemporaries
.

18
. His essay “My Brother Alan” appears in the centenary edition of Sara Turing's book.

19
. Quoted in Lavington (ed.),
Alan Turing and His Contemporaries.

20
. You can hear them at
http://www.digital60.org/media/mark_one_digital_music
.

21
. Turing's secretary in Manchester recalls that his handwriting was so bad that often he could not read it himself, and had to ask her to decipher it.

22
. He wrote to his brother after the arrest to seek his help and advice. The first sentence of the letter read: “I suppose you know I am a homosexual.” But “I knew no such thing,” says John. Turing's colleague Donald Michie has commented (see Sara Turing,
Alan M. Turing
) that Alan was “so child-like and fundamentally good as to make him a very vulnerable person in a world so largely populated by self-seekers.”

CHAPTER 2: VON NEUMANN AND THE MACHINES

1
. This wasn't unusual. As late as the 1920s, the going rate for a knighthood in the UK was about £5,000.

2
. Interview quoted by Dyson.

3
. Eugene Wigner, who would later be awarded the Nobel Prize for his work in theoretical nuclear physics, was a year ahead of von Neumann at the same school.

4
. Interview with George Dyson,
Darwin among the Machines
.

5
. We don't know even today what he had been up to in England, but he later wrote (see Dyson,
Darwin among the Machines
) that “I received in that period a decisive impulse which determined my interest in computing machines.” Given that he already knew Turing, I think we can put two and two together.

6
. See Hargittai,
Martians of Science
.

7
. Quoted by Truesdell,
The Development of Punch Card Tabulations
.

8
. Watson was the head of IBM at the time.

9
. Bizarrely, Zuse's application for a patent on the Z3 was turned down on the basis that it “lacked inventiveness.”

10
. This is important in radar.

11
. Interview in Abramson,
Zworykin, Pioneer of Television
.

12
. Goldstine,
The Computer from Pascal to von Neumann
.

13
. This method of sharing data and programs became common; two decades later,
the data I used for the work on my PhD, carried out on an IBM 360 machine, was sent from California to Cambridge in the same form, although requiring rather fewer cards.

14
. Quoted by Dyson,
Darwin among the Machines
. Goldstine, always more generous to his mentor, says that it was von Neumann “who took the raw idea and perfected it,” and who “crystallized thinking in the field of computers as no other person ever did” (
The Computer from Pascal to von Neumann
). True, but he could have been more generous in sharing the credit.

15
. Goldstine,
The Computer from Pascal to von Neumann
.

16
. Goldstine tells us that von Neumann “had a profound concern for automata. In particular, he always had a deep interest in Turing's work.” Similar mathematical ideas to Turing's had been published in the same year as “On Computable Numbers” by Emil Post, of the City College of New York. However, “There is no doubt that von Neumann was thoroughly aware of Turing's work but apparently not of Post's” (Goldstine,
The Computer from Pascal to von Neumann
).

17
. Mostly because they are outside my area of competence.

18
. Von Neumann's thoughts on self-reproducing automata were gathered in a posthumous book,
Theory of Self-Reproducing Automata
, edited by Arthur Burks, from which his words in this section are taken.

19
. Originally a BBC TV series; now available in book form.

20
. Quoted by Leavitt,
The Man Who Knew Too Much
(my emphasis).

21
. McCarthy and Shannon (eds.),
Automata Studies
.

FIRST INTERLUDE: CLASSICAL LIMITS

1
. In 1997, Moore came up with another striking analogy. The total number of transistors on all of the chips manufactured by Intel in that year was roughly equal to the number of ants on Earth, about 100 million billion.

2
. Actually, not so rapidly, as progress is beginning to slow down as the limits of Moore's Law are approached.

3
. Available at
http://www.zyvex.com/nanotech/feynman.html
.

CHAPTER 3: FEYNMAN AND THE QUANTUM

1
. For the purposes of this book, the terms “quantum mechanics” and “quantum physics” are synonymous.

2
. Mehra,
The Beat of a Different Drum
.

3
. In the US system, “senior” is essentially synonymous with third year undergraduate.

4
. Mehra,
The Beat of a Different Drum
.

5
. Actually, not quite at a definite point. Heisenberg also discovered that no quantum entity can exist at a definite point: there is always some uncertainty in its position. This is a real, intrinsic uncertainty, not the result of our imperfect measurements; the electron itself does not “know” precisely where it is at any moment in time. But we can ignore this Heisenberg uncertainty for the present discussion, because it is very small in these circumstances.

6
. Feynman,
Lectures on Physics
, vol. 3.

7
. Feynman,
Lectures on Physics
, vol. 3.

8
. Reprinted in the volume edited by Laurie Brown,
Selected Paper
s
of Richard Feynman
.

9
. Honesty compels me to say that this is not quite like the kick of a rifle, but the image is a helpful one.

10
. Strictly, the equations now known as Maxwell's equations are a tidied-up version of what he discovered.

11
. Dirac's paper is reprinted at the end of the book
Feynman's Thesis
; his insight can also be found in his textbook
The Principles of Quantum Mechanics
, published by Clarendon Press, Oxford, in 1935 (2nd edn.), but this is too technical for the non-specialist.

12
. It is always important to stress that no such experiment has ever been carried out with a real cat.

13
. See Leff and Rex,
Maxwell's Demon
; this also includes the 1961 paper.

14
. See Leff and Rex,
Maxwell's Demon
, ch. 4.8; this collection also includes the 1973 paper.

15
. See Wright,
Three Scientists and their Gods.

16
. Feynman,
Lectures on Computation
.

17
. Reprinted in Feynman,
Lectures on Computation
.

18
. The Controlled NOT, or CNOT, gate is particularly important in quantum computation, playing a similar role to Fredkin gates in classical computation. It is possible to build any logic circuit using combinations of CNOT gates. See Chapter 5.

CHAPTER 4: BELL AND THE TANGLED WEB

1
. A term first used, in this sense, by Schrödinger in 1935, and presented in the same paper as his cat puzzle. He described the “entangling” of two quantum wave functions as “the characteristic of quantum mechanics [that] enforces its entire departure from classical lines of thought.”

2
. Louis inherited the title “Duc” when his brother died in 1960.

3
. In a talk celebrating de Broglie's 90th birthday in 1982: CERN TH 3315.
A version of this is available in Bell,
Speakable and Unspeakable in Quantum Mechanics
.

4
. Bell,
Speakable and Unspeakable in Quantum Mechanics
.

5
. Somewhat more surprisingly, it wasn't even included in the collection of papers about quantum theory and measurement edited by Wheeler and Zurek and published in 1983.

6
. See Wheeler and Zurek,
Quantum Theory and Measurement
.

7
. In a letter to Max Born.

8
. The year 1935 was, of course, also the year that Schrödinger published his cat “paradox,” discussed in Chapter 3. But at that time Einstein and Schrödinger were essentially the only ones questioning the Copenhagen Interpretation.

9
. Much later, Einstein expressed this idea forcefully in a conversation with Abraham Pais. “Do you really believe,” he asked, “that the Moon exists only when I look at it?” See
Reviews of Modern Physics
, vol. 51 (1979), p. 863.

10
. Because, of course, the effect is not local, but at a distance.

11
. See Hiley and Peat (eds.),
Quantum Interpretations
.

12
. Bell quotes in this section from Bernstein,
Quantum Profiles
, unless otherwise indicated.

13
. My emphasis.

14
. And also in my own
Schrödinger's Kittens
.

15
. See Davies and Brown,
The Ghost in the Atom
.

16
. See Whitaker,
The New Quantum Age
.

17
. See Niels Bohr archive,
http://www.aip.org/history/ohilist/25643.html
.

18
. In the Bohr archive interview, in 2002, Shimony described Bell as “awesome,” saying: “He was discontented with a solution that was hand waving. He was one of the most rigorously honest men ever.”

19
. See Niels Bohr archive,
http://www.aip.org/history/ohilist/25096.html
.

20
. See Bell,
Speakable and Unspeakable in Quantum Mechanics
, ch. 16.

21
. See Bertlmann and Zeilinger (eds.),
Quantum (Un)speakables
.

22
. Davies and Brown,
The Ghost in the Atom
.

SECOND INTERLUDE: QUANTUM LIMITS

1
. That's one hundred billion billion Planck lengths in everyday language.

2
. Feynman,
Lectures on Computation
.

CHAPTER 5: DEUTSCH AND THE MULTIVERSE

1
. Bell,
Speakable and Unspeakable in Quantum Mechanics
, ch. 15.

2
. For sources and more detail on this and the Multiverse idea in general, see my book
In Search of the Multiverse
.

3
. Bell,
Speakable and Unspeakable in Quantum Mechanics
, ch. 20.

4
. Bell,
Speakable and Unspeakable in Quantum Mechanics
, ch. 20.

5
. See Woolf (ed.),
Some Strangeness in the Proportion
.

6
. Remember that FAPP it doesn't matter which version of quantum mechanics you choose to work with; see my book
Schrödinger's Kittens
. It is possible to “explain” quantum computing in other interpretations, but MWI seems the most natural to me, so I will use it from here on.